Question 78884

{{{ 3 ^ sqrt(2x + 3) = sqrt(x-7) }}}

I have never seen an equation like this solved.  You could find some kind of numeric solver to find a numeric solution.  I don't think you can do it with the kind of algebra most people know.  Maybe Ramanujan would have been able to see it.

Exponential decay happens when something is disappearing at a rate that is proportional to the amount that is remaining.  So as there is less and less of it, it disappears slower and slower.  For example, if there is x amount of radioactive substance found in a material at the time it died, and the amount keeps decreasing by 0.003 per year (times the amount that there is), that is exponential decay.  The equation looks like

x(t) = x(0) e^(-0.003 t)

where t is in years, and e^u is the exponential function, and e is the natural base for logarithms.